Collaborative Research: Mechanics of Knots and Tangles of Elastic Rods

合作研究：弹性杆结和缠结的力学

• 批准号: 2101751
• 负责人: Mohammad Khalid Jawed
• 金额: $ 36万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-10-01 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2101751&HistoricalAwards=false
• 关键词: Collaborative; Research; Mechanics; Knots; Tangles

In settings from shipping to sailing to surgery, thousands of different types of knots are used every day, each requiring a specific amount of force to tighten. This force depends on the material properties, friction, and the topology of the knot. A knot typically also has a load-bearing capacity; force beyond this level causes the knot to be undone, and excessive force may result in material failure in the knot. Moreover, some knots hold tight without any external force while others easily get untangled. In other words, the knots can store energy in the material. This concept is called a topological battery with implications in nanometer-sized knots in DNA to macroscopic knots in structural engineering. This award supports research to understand the fundamental science of knots. The work will develop modeling and computational methods for the analysis of the mechanics of knots and tangles. In parallel, it will formulate experimental techniques to systematically study this mechanics. The research will be complemented by developing teaching tools (videos, notes, and demonstrations) for undergraduate and graduate courses. The computational software will also be made publicly available. The research objective of this project is to quantify the mechanical response of knots tied in elastic rods. The project will employ (1) fast numerical simulations inspired by computer graphics, (2) innovative materials with customizable friction, and (3) autonomous robotic experiments to untangle the mechanics of knots. Even in the case of the most basic type of knots (overhand knots), the force required to tie the knot depends on an intricate interplay of (1) elasticity, (2) friction, and (3) topology. Interestingly, the overhand knot may undergo a snap-through buckling instability beyond a critical amount of pull. Such instability in a basic knot points to the richness of the mechanical behavior of knots. After developing simulation and experimental tools, the mechanical response and instabilities of a few common knots, e.g. overhand and shoelace knots, will be investigated. Exploiting the computational speed of the simulation tool and autonomy of robotic experiments, the mechanical response of several types of knots will be quantified to build a library of their mechanics. This data will be used to rationalize the variation of a knot’s mechanical response as a function of the topological, material, and frictional parameters. Similar to the periodic table of elements, a mechanics-based classification scheme of knots will be formulated, where the knots will be grouped into various classes, such as, friction-dominated knots, bending-dominated knots, and others.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

从航运到航行再到手术，每天都会使用数千种不同类型的结，每种结都需要特定的力量来拉紧。该力取决于材料特性、摩擦力和结的拓扑结构。结通常还具有承载能力；超过此水平的力会导致结解开，而过大的力可能会导致结中的材料损坏。此外，有些结不需要任何外力就能紧紧地固定，而另一些结则很容易解开。换句话说，结可以在材料中储存能量。这个概念被称为拓扑电池，其影响范围从 DNA 中的纳米级结到结构工程中的宏观结。该奖项支持了解绳结基础科学的研究。这项工作将开发用于分析结和缠结力学的建模和计算方法。与此同时，它将制定实验技术来系统地研究这种力学。该研究将通过开发本科生和研究生课程的教学工具（视频、笔记和演示）来补充。计算软件也将公开提供。该项目的研究目标是量化弹性杆上打结的机械响应。该项目将采用（1）受计算机图形学启发的快速数值模拟，（2）具有可定制摩擦力的创新材料，以及（3）自主机器人实验来解开结的力学。即使是最基本的结类型（反手结），打结所需的力也取决于 (1) 弹性、(2) 摩擦力和 (3) 拓扑结构的复杂相互作用。有趣的是，超过临界拉力时，正结可能会经历突然的屈曲不稳定性。基本结的这种不稳定性表明了结的机械行为的丰富性。在开发了模拟和实验工具后，一些常见结的机械响应和不稳定性，例如，反手和鞋带打结，将被调查。利用模拟工具的计算速度和机器人实验的自主性，将量化几种类型结的机械响应，以建立其力学库。该数据将用于合理化结的机械响应随拓扑、材料和摩擦参数变化的变化。与元素周期表类似，将制定基于力学的结分类方案，将结分为不同类别，例如摩擦主导结、弯曲主导结等。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Systematic Variation of Friction of Rods

杆摩擦力的系统变化

• DOI: 10.1115/1.4055544
• 发表时间: 2022
• 期刊: Journal of Applied Mechanics
• 作者: Ibrahim Khalil, Md;Tong, Dezhong;Wang, Guanjin;Khalid Jawed, Mohammad;Khoda, Bashir
• 通讯作者: Khoda, Bashir

A Fully Implicit Method for Robust Frictional Contact Handling in Elastic Rods

• DOI: 10.1016/j.eml.2022.101924
• 发表时间: 2022-05
• 期刊: ArXiv
• 作者: Dezhong Tong;Andrew Choi;Jungseock Joo;M. Jawed

Automated Stability Testing of Elastic Rods With Helical Centerlines Using a Robotic System

使用机器人系统对具有螺旋中心线的弹性杆进行自动稳定性测试

• DOI: 10.1109/lra.2021.3138532
• 发表时间: 2022
• 期刊: IEEE Robotics and Automation Letters
• 影响因子: 5.2
• 作者: Tong, Dezhong;Borum, Andy;Jawed, Mohammad Khalid
• 通讯作者: Jawed, Mohammad Khalid

Snap Buckling in Overhand Knots

反手结中的卡扣屈曲

• DOI: 10.1115/1.4056478
• 发表时间: 2023
• 期刊: Journal of Applied Mechanics
• 作者: Tong, Dezhong;Choi, Andrew;Joo, Jungseock;Borum, Andy;Khalid Jawed, Mohammad
• 通讯作者: Khalid Jawed, Mohammad

Ballooning in Spiders using Multiple Silk Threads

• DOI: 10.1103/physreve.105.034401
• 发表时间: 2021-12
• 期刊: Physical review. E
• 作者: C. Habchi;M. Jawed